How to add contextual follow up like Google Assistant
You would need to keep track of the current topic, and references. So, for example, a query When is the next train from London to Birmingham? would result in


topic = TRAIN_TRAVEL
start-loc = London
destination-loc = Birmingham


A follow-up And what about Bristol? would then replace destination-loc with "Bristol" and you would be able to build a new query from that.

The key issues here are the set of topics your assistant will be able to handle, and the relevant object slots. You might also want to clear the topic variable after the next input or so to avoid having it still hanging around even though the user no longer talks about that particular topic. 

UPDATE: Just to add how that would work from a technical point of view. The input And what about Bristol? would not be recognised as any known intent, as it is too unspecific. As a fallback your Assistant then takes the last topic, and interprets the input in the light of that context. So here we assume that the intent is 'train travel', as that is the last thing the user spoke about. This will of course not always work, but should sort out the majority of cases.